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arXiv:2409.09885 · Optica

Accurate vector optically pumped magnetometer with microwave-driven Rabi frequency measurements

Christopher Kiehl, Thanmay S. Menon, Svenja A. Knappe, Tobias Thiele, Cindy A. Regal

Published Dec 11, 2024• 10 citations
arXivHTMLPDF

Abstract

Robust calibration of vector optically pumped magnetometers (OPMs) is a nontrivial task, but increasingly important for applications requiring high-accuracy such as magnetic navigation, geophysics research, and space exploration. Here, we showcase a vector OPM that utilizes Rabi oscillations driven between the hyperfine manifolds of 87 Rb to measure the direction of a DC magnetic field against the polarization ellipse structure of a microwave field. By relying solely on atomic measurements—free-induction decay (FID) signals and Rabi measurements across multiple atomic transitions—this sensor can detect drift in the microwave vector reference and compensate for systematic shifts caused by off-resonant driving, nonlinear Zeeman (NLZ) effects, and buffer gas collisions. To facilitate deadzone-free operation, we also introduce a Rabi measurement that utilizes dressed-state resonances that appear during simultaneous Larmor precession and Rabi driving (SPaR). These measurements, performed within a microfabricated vapor cell platform, achieve an average vector accuracy of 0.46 mrad and vector sensitivities down to 11µrad/Hz for geomagnetic field strengths near 50 µT. This performance surpasses the challenging 1-deg (17 mrad) accuracy threshold of several contemporary OPM methods utilizing atomic vapors with an electromagnetic vector reference.

DOI
10.1364/optica.542502

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Robust calibration of vector optically pumped magnetometers (OPMs) is a nontrivial task, but increasingly important for applications requiring high-accuracy such as magnetic navigation, geophysics research, and space exploration. Here, we showcase a vector OPM that utilizes Rabi oscillations driven between the hyperfine manifolds of 87 Rb to measure the direction of a DC magnetic field against the polarization ellipse structure of a microwave field. By relying solely on atomic measurements—free-induction decay (FID) signals and Rabi measurements across multiple atomic transitions—this sensor can detect drift in the microwave vector reference and compensate for systematic shifts caused by off-resonant driving, nonlinear Zeeman (NLZ) effects, and buffer gas collisions. To facilitate deadzone-free operation, we also introduce a Rabi measurement that utilizes dressed-state resonances that appear during simultaneous Larmor precession and Rabi driving (SPaR). These measurements, performed within a microfabricated vapor cell platform, achieve an average vector accuracy of 0.46 mrad and vector sensitivities down to 11µrad/Hz for geomagnetic field strengths near 50 µT. This performance surpasses the challenging 1-deg (17 mrad) accuracy threshold of several contemporary OPM methods utilizing atomic vapors with an electromagnetic vector reference.
We demonstrate how to measure in situ for heading errors of optically pumped magnetometers (OPMs) in the challenging parameter regime of compact vapor cells with imperfect optical pumping and high buffer gas pressure. For this, we utilize microwave-driven Ramsey and Rabi frequency spectroscopy (FS) to independently characterize scalar heading errors in free-induction-decay (FID) signals. Both of these approaches suppress 5-nT inaccuracies in geomagnetic fields caused by nonlinear Zeeman shifts in FID measurements to below 0.6 nT. For Ramsey FS, we implement short periods of microwave interrogation within a $\ensuremath{\pi}/2\text{\ensuremath{-}}{t}_{R}\text{\ensuremath{-}}3\ensuremath{\pi}/2$ Ramsey interferometry sequence, effectively circumventing systematic errors from off-resonant driving. Conversely, Rabi FS leverages an atom-microwave Hamiltonian for accurate modeling of Rabi oscillation frequencies, achieving a measurement precision down to 80pT/Hz80\phantom{\rule{0.2em}{0ex}}\mathrm{pT}/\sqrt{\text{Hz}}80pT/Hz​ that is limited primarily by technical microwave noise. We show that the fundamental sensitivity of Rabi FS is 30pT/Hz30\phantom{\rule{0.2em}{0ex}}\mathrm{pT}/\sqrt{\text{Hz}}30pT/Hz​ with our vapor cell parameters through a Cram\'er-Rao lower-bound analysis. This work paves the way for future investigations into the accuracy of hyperfine structure magnetometry and contributes to the broader applicability of OPMs in fields ranging from navigation and geophysics to space exploration and unexploded ordinance detection, where heading error mitigation is essential.
Accurate magnetic field direction sensing in compact platforms is critical in applications spanning magnetic navigation, space science, and biomedical imaging. We demonstrate a single-optical-axis vector optically pumped magnetometer based on Rabi oscillations between Zeeman sublevels driven by a series of resonant radiofrequency (RF) polarization ellipses (PEs). A calibration protocol based on controlled rotations of the DC magnetic field determines the spatial orientation of each PE. We develop a detailed theoretical model describing the angular dependence of the Rabi frequencies, incorporating key systematics including RF Stark shifts and Bloch-Siegert shifts. We also account for an RF-based heading-error systematic affecting Rabi-frequency measurements arising from the nonlinear Zeeman effect. Simultaneous Larmor measurements yield the magnitude of the magnetic field, enabling integrated vector-scalar measurements. The magnetometer achieves deadzone-free vector operation with 80 μμμrad mean angular accuracy and angular noise densities as low as 8 μμμrad/Hz/\sqrt{\mathrm{Hz}}/Hz​, offering a pathway towards miniaturized sensors without requiring 3D optical access or sensor rotations.
Atomic magnetometers are highly sensitive instruments widely used for measurements of weak magnetic field. Extracting vector information while maintaining high-precision scalar detection has become the trend in atomic magnetometer development. We introduce a vector atomic magnetometer containing a 5 mm-thick microfabricated vapor cell operating in free-induction-decay mode. By employing orthogonal modulation techniques, the system achieves high-precision in-plane vector magnetic field measurements. The high-precision vector magnetic field measurements are demonstrated in the x–z plane. The sensitivity of the total field detection in the miniaturized atomic magnetometer is 30 pT·Hz−1/2 @11 µT. The average angular error of the decoupled measurement is as low as 4.7 mrad @7.6 µT for vector magnetic fields, providing a new approach for vector magnetic field measurement in miniaturized atomic magnetometers.
The optically pumped magnetometer (OPM) is a class of atomic devices that rely on the measurement of Larmor precession of an atomic spin ensemble in a magnetic field. They need the specific frequency light to complete the pumping and detection process. OPMs typically work under the Earth's magnetic field or a limited field. When operating in near-zero field, they can realize the spin-exchange relaxation-free (SERF) regime, thereby promoting a substantial increase in sensitivity. At present, OPMs have been widely used in magnetoencephalography, magnetocardiography, geomagnetic detection, and inertia measurement (comagnetometer). There are a large number of researchers engaged in the study of relevant mechanisms, devices, technologies, and applications. More importantly, supported by MEMS technology and micro/nano optics, OPMs have the potential to move toward chip-scale sensors. This special issue contains some latest developments in OPMs and related areas. We hope the reprint can provide valuable references for researchers in the related field.
We demonstrate an optically pumped magnetometer (OPM) operated in a free-induction-decay (FID) configuration that is capable of tracking oscillating magnetic signals in the presence of a 50 μT static field. Excellent waveform reconstruction is demonstrated for low frequency modulations with respect to the Nyquist limited bandwidth. A 100 pT oscillation was successfully reconstructed using signal averaging, and an optimum sensitivity of 3.9 pT/Hz was measured from the spectrum of the residuals relative to the sinusoidal fit. The impact of the pump-probe repetition rate and spin depolarization on the frequency response of the sensor is investigated in detail using miniaturized vapor cell technology, with the (-3 dB) bandwidths residing beyond the Nyquist limit in each case. We also discuss technical limitations associated with the magnetometer when exposed to oscillating fields of sufficiently high amplitude or frequency. This is discussed in the context of potential distortions arising in the reproduced signals, induced by frequency modulation (FM) and aliasing artefacts.
The Svenja and Regal research groups are collaboratively advancing the development of scalar and vector magnetometers, including integrated vector-scalar systems. This thesis focuses on designing a compact optically pumped vector magnetometer (COPVM) that measures the orientation of the magnetic field through Rabi frequencymeasurements driven by a microwave field, serving as an electromagnetic vector reference, across multiple atomic transitions. We transformed a large optical table setup for the vector magnetometer, designed by Cindy's group, into a 20 cm by 10 cm rectangular optical breadboard, designing and fabricating essential components like optical mounts, a microwave cavity, a thermal oven, Kapton heaters, and photodiode electronics to meet the dimensional constraints of COPVMs. To improve temperature uniformity in the vapor cell, we propose a novel cylindrical oven design supported by thermal simulations and in-situ experimental measurements of the vapor cell's heating temperature. We also designed a low-magnetic polyimide heater to mitigate magnetic field interference caused by conventional electrical heating elements. Additionally, we developed a compact cubic dielectric cavity (15 x 15 x 15 mm) with feeding loop antennas as a microwave source to drive various hyperfine 87Rb transitions (σ± and π). This project analyzes miniaturization challenges for the compact physics package (CPP) and its impact on size, weight, and power (SWaP), aiming to maintain optimal functionality. Components like optics mounts and microwave cavities are fabricated from nonmetallic materials using advanced techniques such as selective laser sintering (SLS) and CNC machining, which reduce magnetic interference and enhance structural alignment. This approach also allows for customization and rapid adjustments, supporting flexible prototyping and optimization. This thesis provides a roadmap for designing a compact optically pumped vector magnetometer, addressing key challenges and laying the foundation for future advancements in miniaturized atomic sensors.